The everting catheter has been shown to be a reliable clinical means to catheterize long, small diameter, and highly tortuous blood vessels, inaccessible by previous techniques. An everting element evaginates from the tip of a conventional catheter. This extremely flexible polyurethane element has been fabricated in 3, 4 and 5 French sizes, mated with 5, 6 and 7 French catheters, respectively, and is capable of eversion lengths in excess of 40 cm. The catheter has been applied clinically for the local delivery of drugs to brain tumors and embolizing agents to the liver. In the former, treatment is provided by positioning the conventional catheter in the internal carotid artery from a femoral entry, everting the element through the carotid sinus (beyond the ophthalmic artery to avoid retinal toxicity) and perfusing the tumor through the middle and/or anterior cerebral.